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Mazur intersection properties and differentiability of convex functions in Banach spaces

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Georgiev, P. G. and Granero, A. S. and Jiménez Sevilla, María del Mar and Moreno, José Pedro (2000) Mazur intersection properties and differentiability of convex functions in Banach spaces. Journal of the London Mathematical Society, 61 (2). pp. 531-542. ISSN 0024-6107

Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=53605




Abstract

It is proved that the dual of a Banach space with the Mazur intersection property is almost weak* Asplund. Analogously, the predual of a dual space with the weak* Mazur intersection property is almost Asplund. Through the use of these arguments, it is found that, in particular, almost all (in the Baire sense) equivalent norms on [script l]1(Γ) and [script l][infty infinity](Γ) are Fréchet differentiable on a dense Gδ subset. Necessary conditions for Mazur intersection properties in terms of convex sets satisfying a Krein–Milman type condition are also discussed. It is also shown that, if a Banach space has the Mazur intersection property, then every subspace of countable codimension can be equivalently renormed to satisfy this property.


Item Type:Article
Subjects:Sciences > Mathematics > Algebra
ID Code:22200
Deposited On:03 Jul 2013 17:31
Last Modified:01 Feb 2016 16:11

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